AXY-wing (45-6) vertex (45)r7c4, pincers (46)r6c4 & (56)r9c5 with fin (8)r6c4 (marked with #)
If xy-wing is true (r6c4=46): r5c5<>6=4
If fin is true then r6c4=8, then r6c3<>8=5, then r7c3<>5, then r7c4=5, then r9c5<>5=6, then r5c5<>6=4

Ted

[A friendly PM pointed out a typo that I edited marked in red: was r7c5, corrected to r7c4.]

Last edited by tlanglet on Sun Mar 13, 2011 12:53 pm; edited 1 time in total

Ted: I don't really get that "almost xy wing". Why does R6C4 have to be a 46 or an 8 - why not a 48 or a 68. And if one has to follow on with all those "ifs" - is it really a one stepper?

I am sure that others can provide the fundamental math/logic explanation, but here is my "working" view.

In fact, r6c4 does NOT have to be a 46 or an 8, but it MAY be treated as a 46 or an 8! If you prefer, you could also view it as a 48 and a 6 or 68 and a 4. Any grouping of digits within a cell may be formed including each digit individually. Grouping r6c4=46 or r6c4=8 is useful in this puzzle since it then provides part of a xy-wing pattern.

Grouping of cells in an integral part of handling Type n URs. Consider the following Type 3 UR pattern.

Again, I can't provide the gory details as to why you can group digits in any arbitrary manner, but you may. Simply group them in the way that is beneficial to you; just remember that the implication of using all the digits must be considered.

r6c4 is never going to "be" 46 ... or 48 or 68 for that matter. It is going to be exactly one of the candidate set {468}. It is not neccesary to consider every permutation of pairs in the candidate set, only to make sure each candidate occurs at least once in the streams you consider.

In "almost pattern" logic one of the digits (the "fin") is usually the start of some chain or other.. this leaves a reduced candidate set that matches a shortcut we think of as a "pattern" e.g. xywing in this case.

In "kraken" logic each digit is usually considered one at a time - which you could do in this case by following each digit after the fin down to each pincer of the wing.

(I saw an unusual case recently where {ABC} could be treated as {AB} to make an xy-wing and {BC} to make a w-wing. This is fine even though B is used twice - it just means if you followed the kraken logic you have two chains to make the elimination starting with B.)
Enough....!

Thanks Ted and Peterj - I appreciate the detailed responses - but to be honest, for me, these solutions go from fun to painful. In fact after 4 years I’m even wondering whether the Daily Sudukos even need a forum – since the daily solutions are invariably basic "wings and things" - and the more complex solutions generate a very minimal and esoteric response.